Unitary equivalences for essential extensions of $C^*$-algebras
| dc.creator | Lin, Huaxin | |
| dc.date | 2004-03-15 | |
| dc.date.accessioned | 2026-07-07T05:06:24Z | |
| dc.date.available | 2026-07-07T05:06:24Z | |
| dc.description | Let $A$ be a unital separable \CA and $B=C\otimes {\cal K},$ where $C$ is a unital \CA. Let $τ: A\to M(B)/B$ be a weakly unital full essential extensions of $A$ by $B.$ We show that there is a bijection between a quotient group of $K_0(B)$ onto the set of strong unitary equivalence classes of weakly unital full essential extensions $σ$ such that $[σ]=[τ]$ in $KK^1(A, B).$ Consequently, when this group is zero, unitarily equivalent full essential extensions are strongly unitarily equivalent. When $B$ is a non-unital but $σ$-unital simple \CA with continuous scale, we also study the problem when two approximately unitarily equivalent essential extensions are strongly approximately unitarily equivalent. A group is used to compute the strongly approximate unitary equivalence classes in the same approximate unitary equivalent class of essential | |
| dc.identifier | https://arxiv.org/abs/math/0403236 | |
| dc.identifier | http://arxiv.org/abs/math/0403236 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70458 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.title | Unitary equivalences for essential extensions of $C^*$-algebras | |
| dc.type | text |